Correlation coefficient between abc and klm

Problem: 1. A portfolio consists of a T-bill with a face amount of \$10,000 and 200 shares of Camel Corp stock priced at \$60 a share. The T-bill matures after 1 yr, and its yield is 9.4%. The expected return on the stocks is 16%, with sigma of 22%. Find E(Rp) and σ(Rp) of the portfolio. The answer is E(Rp) = 13.15%, σ(Rp)= 12.49%.

Please show all work and calculation and formulas to get these answers.

Problem 2. You invest \$6,000 in ABC Corp stock, and \$4,000 in KLM, Inc. The σ(R) of ABC is 0.2 and that of KLM 0.3. You have calculated the σ(Rp) of this portfolio to be 0.21. What is the correlation coefficient between ABC and KLM? The answer is 0.53125.

Problem 3. You invest \$20,000 in Ford stock which has E(R) = 15% and σ(R) = 15%, and \$25,000 in IBM which has E(R) = 12 and σ(R) = 10%. The correlation coefficient between them is .45. Calculate the expected return and sigma of the portfolio in percentage and dollars. The answer is E(Rp)= 13.33% = \$6,000, σ(Rp)= 10.42%=\$4,690.

Problem 4. A portfolio consists of 80 shares of IBM, each costing \$150 and 200 shares of GM, each worth \$80. For IBM, E(R) = 0.1 and σ(R)= 0.2; for GM E(R) = 0.12 and σ(R)= 0.25. The correlation coefficient between the two companies is 0.75. Find the value of E(Rp) and σ(Rp). The answer is E(Rp)= 11.14%, σ(Rp)== 21.47%.

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